New Trends in Discrete Probability and Statistics: A Comprehensive Review

Abstract

In recent years, discrete probability and statistical methods have made impressive developments that keep impacting all kinds of areas which include computer science (in particular, machine learning and finance), epidemiology, cryptography and social network analysis. This paper studies more recent trends of discrete probability via a systematic review on recent trends in Bayesian modeling, non classical distributions, stochastic process, discrete time financial models, as well as probabilistic AI frameworks. Further, we discuss emerging applications in disease modeling, post quantum cryptography, and network science, illustrating how discrete probabilistic methods are converging with deep learning based and hybrid modeling approaches. While highly successful at increasing accuracy, efficiency, and scalability of the predictions, all are still grappling with computational complexity, ethical (as well as interpretable) concerns in probabilistic decision making. This review evaluates the strengths and weaknesses of current model, provides gaps of current research and perspectives on future directions with techniques that are scalable to inference, hybrid probabilistic framework and fairness aware AI model. These studies produce synthesis of important developments and aim to provide researchers, practitioners an overview of modern discrete probability applications and some future research opportunities.